We numerically study coupling of light into silicon (Si) on glass using different square and hexagonal sinusoidal nanotextures. After describing sinusoidal nanotextures mathematically, we investigate how their design affects coupling of light into Si using a rigorous solver of Maxwell's equations. We discuss nanotextures with periods between 350 nm and 1050 nm and aspect ratios up to 0.5. The maximally observed gain in the maximal achievable photocurrent density coupled into the Si absorber is 7.0 mA/cm2 and 3.6 mA/cm2 for a layer stack without and with additional antireflective silicon nitride layers, respectively. A promising application is the use as smooth anti-reflective coatings in liquid-phase crystallized Si thin-film solar cells.